An approximate weight function construction for a hole emanated crack as a sum of an asymptotic term and a correction one is considered. Based on the known approximate fundamental solution for a half-plane with an edge crack the new weight function asymptotic term which satisfies both known solutions for an edge crack in a half-plane and for an inner crack in an infinite plane is proposed. The practical usefulness of the method is demonstrated for a hole emanated crack in an infinite plate and for a thick cylinder with an edge crack at the inner surface.